document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1121445>Question 1121445</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the exact value of the integral cosx-cos^2(x) in terms of x from x=0 to x=pi/2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #737429 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=737429\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \int^{\small{\pi/2}}_{\small{0}}\,\cos(x)\ -\ \cos^2(x)\,dx\">\r<BR>\n" );
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document.write( "Apply linearity:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \int^{\small{\pi/2}}_{\small{0}}\,\cos(x)\ -\ \int^{\small{\pi/2}}_{\small{0}}\,\cos^2(x)\,dx\">\r<BR>\n" );
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document.write( "The first term is a standard integral, I'll leave that to you.  Use the reduction formula for the second term:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \int\,\cos^n(x)\,dx\ =\ \(\frac{n-1}{n}\,\int\,\cos^{n-2}(x)\,dx\)\ +\ \frac{\cos^{n-1}(x)\sin(x)}{n}\">\r<BR>\n" );
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document.write( "And for this problem <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\ =\ 2\">, hence the antiderivative for the second term is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\cos(x)\sin(x)\ +\ x}{2}\ +\ C\"> \r<BR>\n" );
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document.write( "You can do your own arithmetic<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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